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Class Index | File Index
Elements
Classes

Element ImplicitCurve

JXG.GeometryElement
   ↳ JXG.Curve
         ↳ ImplicitCurve

From Wikipedia: "An implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the unit circle is defined by the implicit equation x2 + y2 = 1. In general, every implicit curve is defined by an equation of the form f(x, y) = 0 for some function f of two variables."

The partial derivatives for f are optional. If not given, numerical derivatives are used instead. This is good enough for most practical use cases. But if supplied, both partial derivatives must be supplied.

The most effective attributes to tinker with if the implicit curve algorithm fails are ImplicitCurve#resolution_outer, ImplicitCurve#resolution_inner, ImplicitCurve#alpha_0, ImplicitCurve#h_initial, ImplicitCurve#h_max, and ImplicitCurve#qdt_box.

Defined in: curve.js.
Extends JXG.Curve.

Element Summary
Constructor Attributes Constructor Name and Description
 
ImplicitCurve
Attributes Summary
Field Attributes Field Name and Description
 
alpha_0
Angle α0 between two successive tangents: determines the smoothness of the curve.
 
delta_0
Allowed distance (in user units) of predictor point to curve.
 
h_critical
If h is below this threshold (in user units), we bail out of the tracing phase of that component.
 
h_initial
Initial step width (in user units).
 
h_max
Maximum step width (in user units).
 
kappa_0
Inverse of desired number of Newton steps.
 
loop_detection
Use Gosper's loop detector.
 
loop_dir
Minimum acos of angle to detect loop.
 
loop_dist
Allowed distance (in user units multiplied by actual step width) to detect loop.
 
margin
Defines the margin (in user coordinates) around the JSXGraph board in which the implicit curve is plotted.
 
max_steps
Maximum iterations for one component of the implicit curve.
 
qdt_box
Half of the box size (in user units) to search for existing line segments in the quadtree.
 
resolution_inner
Vertical resolution (in pixel) to search for components of the implicit curve.
 
resolution_outer
Horizontal resolution: distance (in pixel) between vertical lines to search for components of the implicit curve.
 
tol_0
Tolerance to find starting points for the tracing phase of a component.
 
tol_cusp
Tolerance for cusp / bifurcation detection.
 
tol_newton
Tolerance for the Newton steps.
 
tol_progress
If two points are closer than this value, we bail out of the tracing phase for that component.
Field Summary
Field Attributes Field Name and Description
 
domain
Defines a domain for searching f(x,y)=0.
Method Summary
Method Attributes Method Name and Description
 
dfx()
Partial derivative in the first variable of the left side of the equation f(x,y)=0.
 
dfy()
Partial derivative in the second variable of the left side of the equation f(x,y)=0.
 
f()
Function of two variables for the left side of the equation f(x,y)=0.
Methods borrowed from class JXG.Curve:
addTransform, allocatePoints, generateTerm, getTransformationSource, hasPoint, interpolationFunctionFromArray, maxX, minX, moveTo, notifyParents, update, updateCurve, updateDataArray, updateRenderer, updateTransform, X, Y, Z
Methods borrowed from class JXG.GeometryElement:
_set, addChild, addDescendants, addParents, addParentsFromJCFunctions, addRotation, addTicks, animate, bounds, clearTrace, cloneToBackground, countChildren, createGradient, createLabel, draggable, formatNumberLocale, fullUpdate, generatePolynomial, getAttribute, getAttributes, getLabelAnchor, getName, getParents, getProperty, getSnapSizes, getTextAnchor, getType, handleSnapToGrid, hide, hideElement, noHighlight, normalize, prepareUpdate, remove, removeAllTicks, removeChild, removeDescendants, removeTicks, resolveShortcuts, setArrow, setAttribute, setDash, setDisplayRendNode, setLabel, setLabelText, setName, setParents, setPosition, setPositionDirectly, setProperty, show, showElement, snapToPoints, updateVisibility, useLocale
Events borrowed from class JXG.GeometryElement:
attribute, attribute:key, down, drag, keydrag, mousedown, mousedrag, mousemove, mouseout, mouseover, mouseup, move, out, over, pendown, pendrag, penup, touchdown, touchdrag, touchup, up
Element Detail
ImplicitCurve
This element has no direct constructor. To create an instance of this element you have to call JXG.Board#create with type "implicitcurve".

Possible parent array combinations are:
{Function|String} f

Function of two variables for the left side of the equation f(x,y)=0. If f is supplied as string, it has to use the variables 'x' and 'y'.


{Function|String} dfx

Optional partial derivative in respect to the first variable If dfx is supplied as string, it has to use the variables 'x' and 'y'.


{Function|String} dfy

Optional partial derivative in respect to the second variable If dfy is supplied as string, it has to use the variables 'x' and 'y'.


{Array|Function} rangex

Optional array of length 2 of the form [x_min, x_max] setting the domain of the x coordinate of the implicit curve. If not supplied, the board's boundingbox (+ the attribute "margin") is taken. For algorithmic reasons, the plotted curve mighty slightly overflow the given domain.


{Array|Function} rangey

Optional array of length 2 of the form [y_min, y_max] setting the domain of the y coordinate of the implicit curve. If not supplied, the board's boundingbox (+ the attribute "margin") is taken. For algorithmic reasons, the plotted curve mighty slightly overflow the given domain.


Examples:
  var f, c;
  f = (x, y) => 1 / 16 * x ** 2 + y ** 2 - 1;
  c = board.create('implicitcurve', [f], {
      strokeWidth: 3,
      strokeColor: JXG.palette.red,
      strokeOpacity: 0.8
  });



				
				
 var a, c, f;
 a = board.create('slider', [[-3, 6], [3, 6], [-3, 1, 3]], {
     name: 'a', stepWidth: 0.1
 });
 f = (x, y) => x ** 2 - 2 * x * y - 2 * x + (a.Value() + 1) * y ** 2 + (4 * a.Value() + 2) * y + 4 * a.Value() - 3;
 c = board.create('implicitcurve', [f], {
     strokeWidth: 3,
     strokeColor: JXG.palette.red,
     strokeOpacity: 0.8,
     resolution_outer: 20,
     resolution_inner: 20
 });





				
				
 var c = board.create('implicitcurve', ['abs(x * y) - 3'], {
     strokeWidth: 3,
     strokeColor: JXG.palette.red,
     strokeOpacity: 0.8
 });





				
				
var niveauline = [];
niveauline = [0.5, 1, 1.5, 2];
for (let i = 0; i < niveauline.length; i++) {
    board.create("implicitcurve", [
        (x, y) => x ** .5 * y ** .5 - niveauline[i],
           [0.25, 3], [0.5, 4] // Domain
    ], {
        strokeWidth: 2,
        strokeColor: JXG.palette.red,
        strokeOpacity: (1 + i) / niveauline.length,
        needsRegularUpdate: false
    });
}





				
                

				


			

			


			
				

    				 Attribute Detail
				

				
					 
					


					
					alpha_0

					

					

						Angle α0 between two successive tangents: determines the smoothness of
the curve.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								0.05
							

							

						

					

				
					 
					


					
					delta_0

					

					

						Allowed distance (in user units) of predictor point to curve.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								0.05
							

							

						

					

				
					 
					


					
					h_critical

					

					

						If h is below this threshold (in user units), we bail out
of the tracing phase of that component.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								0.001
							

							

						

					

				
					 
					


					
					h_initial

					

					

						Initial step width (in user units).
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								0.1
							

							

						

					

				
					 
					


					
					h_max

					

					

						Maximum step width (in user units).
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								1
							

							

						

					

				
					 
					


					
					kappa_0

					

					

						Inverse of desired number of Newton steps.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								0.2
							

							

						

					

				
					 
					


					
					loop_detection

					

					

						Use Gosper's loop detector.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								true
							

							

						

					

				
					 
					


					
					loop_dir

					

					

						Minimum acos of angle to detect loop.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								0.99
							

							

						

					

				
					 
					


					
					loop_dist

					

					

						Allowed distance (in user units multiplied by actual step width) to detect loop.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								0.09
							

							

						

					

				
					 
					


					
					margin

					

					

						Defines the margin (in user coordinates) around the JSXGraph board in which the
implicit curve is plotted.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								1
							

							

						

					

				
					 
					


					
					max_steps

					

					

						Maximum iterations for one component of the implicit curve.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								1024
							

							

						

					

				
					 
					


					
					qdt_box

					

					

						Half of the box size (in user units) to search for existing line segments in the quadtree.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								0.2
							

							

						

					

				
					 
					


					
					resolution_inner

					

					

						Vertical resolution (in pixel) to search for components of the implicit curve.
A small number increases the running time. For large number components may be missed.
Minimum value is 0.01.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								5
							

							

						

					

				
					 
					


					
					resolution_outer

					

					

						Horizontal resolution: distance (in pixel) between vertical lines to search for components of the implicit curve.
A small number increases the running time. For large number components may be missed.
Minimum value is 0.01.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								5
							

							

						

					

				
					 
					


					
					tol_0

					

					

						Tolerance to find starting points for the tracing phase of a component.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								JXG.Math.eps
							

							

						

					

				
					 
					


					
					tol_cusp

					

					

						Tolerance for cusp / bifurcation detection.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								0.05
							

							

						

					

				
					 
					


					
					tol_newton

					

					

						Tolerance for the Newton steps.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								1.0e-7
							

							

						

					

				
					 
					


					
					tol_progress

					

					

						If two points are closer than this value, we bail out of the tracing phase for that
component.
						
							

							Defined in:  options.js.
						
						
					


					

						
						
						
						
							

							
Default Value:

							

								0.0001
							

							

						

					
				
			


			
				

                     Field Detail
				

				
					 
					


					
					domain

					

					

						Defines a domain for searching f(x,y)=0. Default is null, meaning
the bounding box of the board is used.
Using domain, visProp.margin is ignored.
						
						
					


					

						
						
						
						

					
				
			


			
				

					Method Detail
				

				
					 
					


					{Number}
					dfx()

					

					

						Partial derivative in the first variable of
the left side of the equation f(x,y)=0.
If null, then numerical derivative is used.
						
						
					


						
						
						
						
						
							

							
Returns:

							
								
{Number} 

							
							

						
						
						

					

					

				
					 
					


					{Number}
					dfy()

					

					

						Partial derivative in the second variable of
the left side of the equation f(x,y)=0.
If null, then numerical derivative is used.
						
						
					


						
						
						
						
						
							

							
Returns:

							
								
{Number} 

							
							

						
						
						

					

					

				
					 
					


					{Number}
					f()

					

					

						Function of two variables for the left side of the equation f(x,y)=0.
						
						
					


						
						
						
						
						
							

							
Returns:

							
								
{Number} 

							
							

						
						
						

					

					
				
			


			

			


			
                
                

                    Attributes borrowed from other Elements
                


                

                
Attributes borrowed from class JXG.Curve: 
lineCap
Attributes borrowed from class JXG.GeometryElement: 
dash, dashScale, draft, dragToTopOfLayer, fillColor, fillOpacity, fixed, frozen, gradient, gradientAngle, gradientCX, gradientCY, gradientEndOffset, gradientFR, gradientFX, gradientFY, gradientR, gradientSecondColor, gradientSecondOpacity, gradientStartOffset, highlight, highlightFillColor, highlightFillOpacity, highlightStrokeColor, highlightStrokeOpacity, highlightStrokeWidth, isLabel, layer, needsRegularUpdate, nonnegativeOnly, precision, priv, rotatable, scalable, shadow, snapToGrid, strokeColor, strokeOpacity, strokeWidth, tabindex, trace, traceAttributes, transitionDuration, transitionProperties, viewport, visible, withLabel

                

                

                


				
				

					Fields borrowed from other Elements
				


				

				
Fields borrowed from class JXG.Curve: 
dataX, dataY, numberPoints, qdt, ticks
Fields borrowed from class JXG.GeometryElement: 
_org_type, _pos, ancestors, baseElement, board, childElements, descendants, dump, elementClass, elType, hasLabel, highlighted, id, inherits, isDraggable, isReal, lastDragTime, methodMap, mouseover, name, needsUpdate, notExistingParents, numTraces, parents, quadraticform, rendNode, stdform, subs, symbolic, traces, transformations, type, visProp, visPropCalc

				

				

				

				
				

					Methods borrowed from other Elements
				

				

				
Methods borrowed from class JXG.Curve: 
addTransform, allocatePoints, generateTerm, getTransformationSource, hasPoint, interpolationFunctionFromArray, maxX, minX, moveTo, notifyParents, update, updateCurve, updateDataArray, updateRenderer, updateTransform, X, Y, Z
Methods borrowed from class JXG.GeometryElement: 
_set, addChild, addDescendants, addParents, addParentsFromJCFunctions, addRotation, addTicks, animate, bounds, clearTrace, cloneToBackground, countChildren, createGradient, createLabel, draggable, formatNumberLocale, fullUpdate, generatePolynomial, getAttribute, getAttributes, getLabelAnchor, getName, getParents, getProperty, getSnapSizes, getTextAnchor, getType, handleSnapToGrid, hide, hideElement, noHighlight, normalize, prepareUpdate, remove, removeAllTicks, removeChild, removeDescendants, removeTicks, resolveShortcuts, setArrow, setAttribute, setDash, setDisplayRendNode, setLabel, setLabelText, setName, setParents, setPosition, setPositionDirectly, setProperty, show, showElement, snapToPoints, updateVisibility, useLocale

				

				

                

                
   				

    				Events borrowed from other Elements
                

                

                
Events borrowed from class JXG.GeometryElement: 
attribute, attribute:key, down, drag, keydrag, mousedown, mousedrag, mousemove, mouseout, mouseover, mouseup, move, out, over, pendown, pendrag, penup, touchdown, touchdrag, touchup, up

                

                

            

		




		

			
			Documentation generated by JsDoc Toolkit 2.4.0 on Wed Oct 23 2024 15:44:12 GMT+0200 (Mitteleuropäische Sommerzeit)